Humphreys, Macartan (2016) Political Games: Mathematical Insights on Fighting, Voting, Lying & Other Affairs of State.​ New York: Norton. 208 pp.​​

​ISBN: 9780393263336​

Han Dorussen

University of Essex

​Macartan Humphreys sets out to identify the most valuable contributions of formal theory to the study of politics. Initially conceived as concise 'notebook', Political Games developed into a collection of 49 brief but tightly structured chapters. Each presents a key insight, the logic behind it, and a concise explanation and technical notes. An imaginative graphic representation accompanies each insight, providing easy accessible and intuitive understanding of the underlying logic. The author has gleaned the key insights from formal theory relying primarily on game the​ory but borrowing liberally from its 'cousins', such as decision theory, social choice theory and spatial theory. The applications are equally broad, from military strategy and international relations to electoral behavior, agenda setting and policy making. Some of the chapters discuss elementary contributions such as Prisoners' Dilemma and Chicken, while others introduce more advanced and less well-known insights such as second-guessing in the k-level model. Underlying assumptions and connections between ideas are highlighted throughout the book. Particularly valuable is the reflection on how further analyses reveal the limits of earlier derived knowledge, for example contrasting the Condorcet Jury Theorem with conformist voting because of information cascades. The book is a useful introduction to formal theory in political science and its many illustrations and examples should be helpful in presenting challenging ideas to students. The introduction suggests pathways and themes for subfields in political science, including international relations and peace studies. The main quality of the book, however, is to highlight the coherent framework underlying the various contributions to these subfields. It is inspiring to see such different insights – some old, some new, some familiar, some surprising – brought together.